SOLUTION: A mathematics problem is given to three students A, B, C whose chances of solving it are 1/4, 2/3, 1/2 respectively. If all of them try independently, the probability that the prob

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Question 1144001: A mathematics problem is given to three students A, B, C whose chances of solving it are 1/4, 2/3, 1/2 respectively. If all of them try independently, the probability that the problem is solved by any one of the students is: -
Answer by ikleyn(52778) About Me  (Show Source):
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HINT.  The probability that the problem will be solved by anyone of the three students is the COMPLEMENT

       to the probability that the problem will not be solved by anyone of them.



SOLUTION


The probability that student A will not solve the problem is  1 - 1%2F4 = 3%2F4.


The probability that student B will not solve the problem is  1 - 2%2F3 = 1%2F3.


The probability that student C will not solve the problem is  1 - 1%2F2 = 1%2F2.


The probability that the problem will not be solved by students A, B, and C  is

    P = %283%2F4%29%2A%281%2F3%29%2A%281%2F2%29 = 1%2F8.


Hence, the answer to the problem question is the COMPLEMENT to  1%2F8,  i.e.   1 - 1%2F8 = 7%2F8.    ANSWER